The scientific research on static buckling and post-buckling behaviour of conservative systems has been carried out for a number of years. Thin-walled plate structures subjected to axial compression may have many different buckling modes. The structures of such a sort are able to sustain load after local buckling mode. The local buckles cause a reduction in stiffness of the section and subsequent lowering of the load carrying capacity with respect to the nonlocally buckled section. The global buckling mode always causes a collapse of thin-walled structures. The phenomenon of interaction between different buckling modes accelerates the destruction of structures. The problem of interaction of the global modes with the local ones is very interesting and of great significance.